I will present two expository lectures on the work of Maulik and Okounkov (http://arxiv.org/abs/1211.1287), focusing on the geometric R-matrix formalism which leads to the construction of a Hopf algebra $Y_Q$ acting on the equivariant cohomology of the Nakajima varieties associated to a quiver $Q$.
In the first lecture, I will give an overview of the stable basis construction in the equivariant cohomology of an algebraic symplectic variety, which is the key technical tool used to construct the geometric R-matrices. I will then present an explicit example of the Maulik-Okounkov construction in the simple case of cotangent bundles to Grassmannians, which will yield a geometric construction of the Yangian of $gl_2$.

I will present two expository lectures on the work of Maulik and Okounkov (http://arxiv.org/abs/1211.1287), focusing on the geometric R-matrix formalism which leads to the construction of a Hopf algebra $Y_Q$ acting on the equivariant cohomology of the Nakajima varieties associated to a quiver $Q$.
In the second lecture, we will see how many features of the Grassmannian example carry over to the more general setting of Nakajima quiver varieties. We will review the definition of these varieties, and present the definition of the Maulik-Okounkov Yangian $Y_Q$ associated to a quiver $Q$. Time permitting, we will outline some ideas on how to extend the Maulik-Okounkov construction to encompass Yangian coideal subalgebras, such as the reflection equation algebra.